R for Art Sundays
Strange Attractors: General 2D Map - Part 1
An R experiment to create images generated by the trajectory of a particle according to a strange attractor.
Made with Rcpp, tidyverse
Blog post explaining the experiment: Rcpp, Camarón de la Isla and the Beauty of Maths
Inspired by: Strange Attractors: Creating Patterns in Chaos, by Julien C. Sprott
library(Rcpp)
library(tidyverse)
opt <- theme(legend.position = "none",
panel.background = element_rect(fill="white", color="black"),
plot.background = element_rect(fill="white"),
axis.ticks = element_blank(),
panel.grid = element_blank(),
axis.title = element_blank(),
axis.text = element_blank())
cppFunction('DataFrame createTrajectory(int n, double x0, double y0,
double a1, double a2, double a3, double a4, double a5,
double a6, double a7, double a8, double a9, double a10,
double a11, double a12, double a13, double a14) {
// create the columns
NumericVector x(n);
NumericVector y(n);
x[0]=x0;
y[0]=y0;
for(int i = 1; i < n; ++i) {
x[i] = a1+a2*x[i-1]+ a3*y[i-1]+ a4*pow(fabs(x[i-1]), a5)+ a6*pow(fabs(y[i-1]), a7);
y[i] = a8+a9*x[i-1]+ a10*y[i-1]+ a11*pow(fabs(x[i-1]), a12)+ a13*pow(fabs(y[i-1]), a14);
}
// return a new data frame
return DataFrame::create(_["x"]= x, _["y"]= y);
}
')
a1 <- -0.8171
a2 <- -0.2079
a3 <- 0.8808
a4 <- -0.7116
a5 <- -1.0024
a6 <- 0.2106
a7 <- -0.7312
a8 <- 1.1553
a9 <- -0.0771
a10 <- -0.81710
a11 <- -0.81711
a12 <- -0.81712
a13 <- -0.81713
a14 <- -0.81714
df <- createTrajectory(10000000, 1, 1, a1, a2, a3, a4, a5, a6,
a7, a8, a9, a10, a11, a12, a13, a14)
mx <- quantile(df$x, probs = 0.05)
Mx <- quantile(df$x, probs = 0.95)
my <- quantile(df$y, probs = 0.05)
My <- quantile(df$y, probs = 0.95)
df %>% filter(x > mx, x < Mx, y > my, y < My) -> df
plot <- ggplot(df) +
geom_point(aes(x, y), shape=46, alpha=0.01, size=0, color="black") +
scale_x_continuous(expand = c(0,0))+
scale_y_continuous(expand = c(0,0))+
coord_fixed() +
opt
plot